A team of the University of Bucharest placed first in the Competition Unbreakable Romania (season spring-summer 2021). Congratulations to Dragos Albastroiu, Mihail Feraru (undergraduates at Faculty of Mathematics and Computer Science), and Andrei Ciobanu (master student enrolled at our Security and Applied Logic master program) for finishing the team competition on the first place! More information available here.

## Unbreakable Romania – Winners

The University of Bucharest is placed in the top for the best score at the Individual Competition Unbreakable Romania (season spring-summer 2021). Congratulations to Dragos Albastroiu, undergraduate at Faculty of Mathematics and Computer Science, for finishing the individual competition on the first place! More information available here.

## Active Defense in Cybersecurity

**Title: **Active Defense in Cybersecurity

**Speaker: **Sergiu Bogdan Meseșan & Andreea Drugă, Cybersecurity Specialists at **ENEA**

**Agenda:**

*Active Defense Mechanisms*– Notions, principles and Active Defense mechanisms (ca.1h)

*Practical Application for Honeypot Analytics and Attacks Data Collection*– Presentation of a platform implemented by ENEA specially for this lecture, a practical demo of Active Defense (ca.1h)

*Active Defense DIY*– Workshop installation, running, Internet access for a Honeypot type VM using an open source platform (Telekom Tpot CE) (ca.1h-1.5h)

**For the students interested to attend the meeting:** please contact Ruxandra Olimid (ruxandra.olimid@fmi.unibuc.ro)

## Kernelization, Proof Complexity and Social Choice

**Title: **Kernelization, Proof Complexity and Social Choice

**Speaker: **Gabriel Istrate (West University of Timișoara)

**Abstract: **

We display an application of the notions of kernelization and data reduction from parameterized complexity to proof complexity: Specifically, we show that the existence of data reduction rules for a parameterized problem having (a) a small-length reduction chain, and (b) small-size (extended) Frege proofs certifying the soundness of reduction steps implies the existence of subexponential size (extended) Frege proofs for propositional formalizations of the given problem. We apply our result to infer the existence of subexponential Frege and extended Frege proofs for a variety of problems. Improving earlier results of Aisenberg et al. (ICALP 2015), we show that propositional formulas expressing (a stronger form of) the Kneser-Lovasz Theorem have polynomial size Frege proofs for each constant value of the parameter k. Previously only quasipolynomial bounds were known (and only for the ordinary Kneser-Lovasz Theorem). Another notable application of our framework is to impossibility results in computational social choice: we show that, for any fixed number of agents, propositional translations of the Arrow and Gibbard-Satterthwaite impossibility theorems have subexponential size Frege proofs.

This is joint work with Cosmin Bonchiș and Adrian Crăciun.

## An Introduction to Protocols in Dynamic Epistemic Logic

**Title: **An Introduction to Protocols in Dynamic Epistemic Logic

**Speaker: **Alexandru Dragomir (University of Bucharest)

**Abstract: **

**References**:

## Regular matching problems for infinite trees

**Title: **Regular matching problems for infinite trees

**Speaker: **Mircea Marin (West University of Timișoara)

**Abstract: **

*Regular algebra and finite machines*and showed that if L and R are regular, then the problem “∃σ:∀x∈X:σ(x)≠∅∧σ(L)⊆R?” is decidable. Moreover, there are only finitely many maximal solutions, which are regular and effectively computable. We extend Conway’s results when L and R are regular languages of finite and infinite trees, and language substitution is applied inside-out. We show that if L⊆T(X) and R⊆T(Σ) are regular tree languages then the problem “∃σ∀x∈X:σ(x)≠∅∧σ

_{io}(L)⊆R?” is decidable. Moreover, there are only finitely many maximal solutions, which are regular and effectively computable. The corresponding question for the outside-in extension σ

_{oi}remains open, even in the restricted setting of finite trees. Our main result is the decidability of “∃σ:σ

_{io}(L)⊆R?” if R is regular and L belongs to a class of tree languages closed under intersection with regular sets. Such a special case pops up if L is context-free.

This is joint work with Carlos Camino, Volker Diekert, Besik Dundua and Géraud Sénizergues.

**References**:

[1] C. Camino, V. Diekert, B. Dundua, M. Marin, G. Sénizergues, Regular matching problems for infinite trees. arXiv:2004.09926 [cs.FL], 2021.

## A proof mining case study on the unit interval

**Title: **A proof mining case study on the unit interval

**Speaker: **Andrei Sipoș (University of Bucharest & IMAR)

**Abstract: **

_{n}), (t

_{n}) ⊆ [0,1] are such that for all n, x

_{n+1}=(1-t

_{n})x

_{n}+t

_{n}f(x

_{n}) and there is a δ>0 such that for all n, t

_{n}≤(2-δ)/(L+1), then the sequence (x

_{n}) converges.

**References**:

*J. Math. Anal. Appl.*157, no. 1, 112–126, 1991.

## Exponential Diophantine equations over ℚ

**Title: **Exponential Diophantine equations over ℚ

**Speaker: **Mihai Prunescu (University of Bucharest & IMAR)

**Abstract:**

In a previous exposition [1] we have seen that the solvability over ℚ is undecidable for systems of exponential Diophantine equations. We now show that the solvability of individual exponential Diophantine equations is also undecidable, and that this happens as well for some narrower families of exponential Diophantine equations.

**References**:

*The Journal of Symbolic Logic*, Volume 85, Issue 2, 671–672, 2020.

## Unbreakable Romania

We are pleased to support UNbreakable Romania – the national competition organised for students in the country preparing for a career in cybersecurity.

- The preparation stage will start on April 1 when the registered participants will have at their disposal theoretical and practical resources that will allow them to become familiar with the format and methodology of the contest.

2. The individual contest will take place between May 14-16.

3. The team competition will take place on June 4-6.

At the end of the season, there will be a national #ROEduCyberSkills ranking that will provide an overview of cybersecurity performance in Romania.

Registration is free and is available on the official website: https://unbreakable.ro/inregistrare

## Unwinding of proofs

**Title: **Unwinding of proofs

**Speaker: **Pedro Pinto (TU Darmstadt)

**Abstract:**

*“What more do we know if we have proved a theorem by restricted means than if we merely know that it is true?”*

In this talk, we set out to give a brief introduction to the proof mining program, focusing on the following points:

- functional interpretations in an introductory way;
- the bounded functional interpretation [3,4];
- a concrete translation example: the metric projection argument.

We finish with a brief discussion of some recent results [5,6].

**References**:

*Applied Proof Theory: Proof Interpretations and their Use in Mathematics*. Springer Monographs in Mathematics. Springer-Verlag Berlin Heidelberg, 2008.

[2] U. Kohlenbach. Proof-theoretic methods in nonlinear analysis. In M. Viana B. Sirakov, P. Ney de Souza, editor,

*Proceedings of the International Congress of Mathematicians – Rio de Janeiro 2018*, Vol. II: Invited lectures, pages 61–82. World Sci. Publ., Hackensack, NJ, 2019.

[3] F. Ferreira and P. Oliva. Bounded functional interpretation.

*Annals of Pure and Applied Logic*, 135:73-112, 2005.

[4] F. Ferreira. Injecting uniformities into Peano arithmetic.

*Annals of Pure and Applied Logic*, 157:122-129, 2009.

[5] B. Dinis and P. Pinto. Effective metastability for a method of alternating resolvents. arXiv:2101.12675 [math.FA], 2021.

[6] U. Kohlenbach and P. Pinto. Quantitative translations for viscosity approximation methods in hyperbolic spaces. arXiv:2102.03981 [math.FA], 2021.

** **

**References**: